Edge Soup: Continuous-Scale Point Cloud Learning with a Single Graph

Point-cloud learning is dominated by hierarchical architectures that explicitly discretize geometric information into a fixed set of scales. We introduce Edge Soup, a graph construction method that instead models scale as a continuous property of nodes within a single graph. By assigning points a scale coordinate and performing a $k$-nearest-neighbor query in an augmented space, we generate a homogeneous "soup" of edges that has connectivity ranging from local to long-range. The resulting graph reproduces structural characteristics of hierarchical representations while requiring only a single graph-construction step. A simple sequential Graph Neural Network (GNN) operating on this graph achieves competitive performance on challenging point-cloud segmentation benchmarks without the need for separate graphs or cross-scale connections like pooling and unpooling. Such a network exhibits increased robustness to density variation, noise, and sampling artifacts, maing it particularly effective on large-scale LiDAR datasets. Because Edge Soup replaces expensive hierarchy construction with a single graph building step, it substantially reduces data preparation overhead and lowers end-to-end inference latency on large point clouds.